Applications of Optimization with XpressMP by Christelle GuA©ret Christian Prins Marc Sevaux

By Christelle GuA©ret Christian Prins Marc Sevaux

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Additional info for Applications of Optimization with XpressMP

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It is easy to see that if we have just one output then this is a simple fixed ratio blending example. Such M-input/N-output constraints often arise where we have a plant that we can operate in different ways (modes), and the ratios differ for different modes. At any point in time, the plant can only be in one mode. Consider a very simple example, where we have 3 inputs, 2 outputs and 3 possible operating modes. e. we have shown the kg of each input used, and output produced, by the plant. The decision variables are the number of hours the plant spends in each mode m, say usemodem .

It would reduce the number of variables a little but we are probably going to have to use these variables somewhere else in the model anyway and so the substitution would have to take place everywhere the ruset variables appeared in the model. The model would certainly be less comprehensible, and consequently harder to maintain. A new form of material balance equations of the multi-period type occurs where we have fixed demands for our product or products in the NT time periods. In other words, the selling decision variables (sellt in the example above) are fixed.

Let us consider the material balance in time period t. ’ We are faced with a slight problem now — we do not know the decision variable for the stock at the beginning of time period t but we can see that, assuming there is no loss of stock, the stock at the beginning of time period t is the same at the end of time period t -1. So in different words, the previous statement can be phrased as ‘the stock at the end of time period t is equal to the stock at the end of time period t − 1, plus what we make in period t, minus what we sell in period t’.